Panconnectivity and edge-pancyclicity of 3-ary N-cubes

Authors:
Sun-Yuan Hsieh;Tsong-Jie Lin;Hui-Ling Huang
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan 70101;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan 70101;Department of Information Management, Southern Taiwan University of Technology, Taiwan, Taiwan 710
Venue:
The Journal of Supercomputing
Year:
2007

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Abstract

We study two topological properties of the 3-ary n-cube Q n 3 . Given two arbitrary distinct nodes x and y in Q n 3 , we prove that there exists an x---y path of every length ranging from d(x,y) to 3 n 驴1, where d(x,y) is the length of a shortest path between x and y. Based on this result, we prove that Q n 3 is edge-pancyclic by showing that every edge in Q n 3 lies on a cycle of every length ranging from 3 to 3 n .